relating a small change in (loge V) or (1/V) , d(loge V) and d(1/V), respectively representing the standard deviations, to the corresponding change in V (Selby 1972, Derivatives 10 and 19). This is a good approximation to one-half the range between the 16th and 84th fractiles. The means, fractiles, multipli-cative factors, and approximate standard deviations are tabulated in Section 6.2.
The reason for using one of these three averaging methods is that there are different interpretations regarding the underlying distribution of values being averaged. In the case of the geometric mean, it assumes that the distribution of velocity values is log-normally distributed and that errors or variability in the values tend to be multiplicative. In the case of the harmonic mean, because velocity is measured by making travel-time measurements, normally distributed errors in the travel-time measurements are introduced into the denominator of the ratio distance/travel time, implying that 1/V is normally distri-buted. In addition, when averaging velocities over multiple adjacent distance intervals, this average preserves the total travel time accumulated from all of the intervals.
All three types of mean are used to estimate average velocities and uncertainties in the basalts and interbeds in Section 6.2 and in the sediments in Section 6.3. The seismic response modeling requires the use of the geometric mean, even though the harmonic mean may be the most appropriate.
Arithmetic means are used for density data in Section 6.4. Laboratory measurements of basalt density (Carmichael 1989) suggest that they have a normal distribution, so the arithmetic mean is appropriate.
Outliers show only lower densities from the main peak in the laboratory data, similar to the borehole measurements made at the WTP site. This is not typical of a log-normal distribution. Section 6.5 uses arithmetic means to develop average densities and density shape factors and uses harmonic means to develop average shape factors for velocity.
Weighted means could be used when there are standard error estimates for each of the measurements.
This would allow for the better-determined values being given more weight. Weighted means can be used regardless of whether the arithmetic, geometric, or harmonic means are considered. In the case of the velocity data (Redpath 2007; Stokoe et al. 2007), no error estimates are given. Layer thicknesses over which velocities are calculated are not highly variable (velocity measured over a longer distance would be more accurate), and data were taken at the same depth spacing so that the number of data points also does not vary. Error estimates for density (MacQueen and Mann 2007) were calculated, but they did not vary significantly. Weighted means have not been used in this analysis.
6.2 Basalt and Interbed Model
The data from the downhole Vs measurements reported in Section 3 are examined and summarized in this section. The travel-time data plots were examined to form velocity profiles to compare the different measurements and the different boreholes. Figure 6.1 shows the Vs profiles at the three new boreholes recorded by Texas. The depth intervals conform to the geophysically picked interfaces between the basalts and interbeds. The data are shown relative to the elevation of the Priest Rapids Member flow top
0 2000 4000 6000 8000 10000
−200 0 200 400 600 800 1000
Shear Wave Velocity, fps
Elevation Above Priest Rapids Basalt, feet
C4993 C4996 C4997
Figure 6.1. Texas Downhole Shear Wave Velocity Profiles
Figure 6.2 shows the data collected by Redpath Geophysics. The impulsive source used here had sufficient power to observe downhole signals to depths of up to 750 ft. In the data, there is evidence for a lower velocity flow top in the Pomona Member for two of the boreholes. This has been difficult to detect with downhole data because of the depth sampling of 5 to 10 ft. This was not well determined, but careful examination of the data by Redpath Geophysics suggests this.
Figure 6.3 compares the Texas and Redpath Geophysics Vs profiles. The Redpath Geophysics Vs in the Elephant Mountain Member (uppermost basalt) are, on average, slightly higher than those measured by Texas, but Vs for the second basalt (Pomona Member) are consistent. The presence of an extensive lower-velocity flow top in the Pomona Member is reflected in Vs values of 5,000 fps in two of the three boreholes.
Figures 6.4 and 6.5 display the basalt and interbed velocities in histogram form for the Texas and Redpath Geophysics data sets, respectively. These form the basis from which to generate average models under various alternative assumptions.
The thicknesses of each basalt and interbed unit from each of the four new boreholes are summarized
0 2000 4000 6000 8000 10000
−200 0 200 400 600 800 1000
Shear Wave Velocity, fps
Elevation Above Priest Rapids Basalt, feet
C4993 C4996 C4997
Figure 6.2. Redpath Downhole Shear Wave Velocity Profiles
0 2000 4000 6000 8000 10000
−200 0 200 400 600 800 1000
Shear Wave Velocity, fps
Elevation Above Priest Rapids Basalt, feet
Texas Redpath
Figure 6.4. Texas Downhole Shear Wave Velocity Measurements
Table 6.1. Thickness Variation in Basalt and Interbed Layers Basalt and Interbed Unit Thicknesses in Feet
C4993 C4996 C4997 C4998
Elephant Mountain Member 118 104 112 110
Rattlesnake Ridge Interbed 56 42 47 34
Pomona Member 186 201 196 209
Selah Interbed 23 22 22 22
Esquatzel Member 95 96 95 94
Cold Creek Interbed 97 91 98 98
Umatilla Member 161 156 161 157
Mabton Interbed 98 96 94 98
Priest Rapids Member, Lolo flow 161 165 156 161 There is very little thickness variation in the lower basalt and interbed layers. The combined thickness of the Rattlesnake Ridge interbed and Pomona Member also is nearly constant, indicating that there is more topography on the interface between them than on the top or bottom of the combined basalt-interbed combination. This can be seen in Figure 6.1, where the interface between the top basalt and the underlying interbed is more variable than the bottom of the interbed.
The range of layer thicknesses in Table 6.1 is used in the seismic response modeling by Youngs (2007). In the modeling, each layer thickness is randomized from a uniform distribution between the maximum and minimum thickness for that layer. In the case of the Rattlesnake Ridge interbed and the Pomona Member, a correlation is introduced into the randomization to keep the combined thickness constant, effectively randomizing only the interface between them.
A number of alternatives to forming average Vs profiles have been suggested. These averaging alternatives are examined in Tables 6.2 through 6.4. The results are dominated by the Texas data due to its extended depth range, but the only evidence for flow tops from downhole measurements comes from the Redpath Geophysics data. Density (Section 5) and suspension logging (Section 3.2) provide strong evidence for reduced velocity in the basalt flow tops. The effect of the flow tops is to smooth out the impedance contrast between the tops of basalt and the overlying interbed. Examination of the geophys-ical data for similar features in the flow bottoms indicated that these are minor (on the order of 1 ft in thickness) or entirely absent, as discussed further in Section 6.4.
Three different averaging methods were used to examine and tabulate the Vs data; the geometric, arithmetic, and harmonic means were introduced in Section 6.1.
Table 6.3 shows the average Vs from Redpath (2007). These data cover only the Elephant Mountain and Pomona members’ flow interiors and the Rattlesnake Ridge interbed between them. In addition, Table 6.3 shows the result of averaging the six Redpath and Texas velocities for these three layers.
Table 6.2. Average Shear Wave Velocities from All Texas Measurements
Stratigraphic Unit
EMM RRI PM SI EM CCI UM MI PRM
Geometric mean (ft/sec) 7574 2752 8299 2946 8287 2697 8362 2723 8042 84th percentile (ft/sec) 8124 3124 8425 3476 8790 2993 8571 2744 8842 16th percentile (ft/sec) 7063 2425 8176 2496 7814 2430 8158 2703 7314 Approx. Vel. Std. Dev.
(ft/sec)
530 348 125 488 488 281 207 21 763
Sigma 0.070 0.127 0.015 0.166 0.059 0.104 0.025 0.008 0.095 Mult. Factor 1.072 1.135 1.015 1.180 1.061 1.110 1.025 1.008 1.100
Arithmetic mean (ft/sec) 7587 2767 8300 2973 8297 2707 8363 2723 8060 84th percentile (ft/sec) 8109 3104 8425 3485 8780 2996 8571 2744 8824 16th percentile (ft/sec) 7065 2429 8175 2462 7813 2417 8155 2703 7296 Std. Dev. (ft/sec) 522 337 125 512 483 289 208 21 764
Harmonic mean (ft/sec) 7562 2737 8299 2920 8278 2687 8360 2723 8024 84th percentile (ft/sec) 8140 3149 8425 3466 8800 2989 8570 2744 8864 16th percentile (ft/sec) 7060 2421 8177 2522 7814 2441 8160 2703 7329 Approx. Vel. Std. Dev.
(ft/sec)
537 358 124 460 492 271 205 21 760
Mult. Fac. High 1.076 1.150 1.015 1.187 1.063 1.112 1.025 1.008 1.105 Mult. Fac. Low 0.934 0.884 0.985 0.864 0.944 0.908 0.976 0.992 0.913 EMM = Elephant Mountain Member; RRI = Rattlesnake Ridge interbed; PM = Pomona Member; SI = Selah interbed; EM = Esquatzel Member; CCI = Cold Creek interbed; UM = Umatilla Member; MI = Mabton interbed; PRM = Priest Rapids Member.
Comparison of the velocities in Table 6.4 should be made to the individual basalt velocity averages in Table 6.2, in particular the Elephant Mountain Member that was excluded in this average. The Elephant Mountain Member appears to have a consistently lower velocity than the deeper basalt layers in the data from Texas. In addition, Table 6.4 shows the effect of averaging all of the basalt velocities as a single velocity and all of the interbeds as a single velocity.
The standard errors or ranges from the different averaging methods generally are comparable and do not indicate that any one of them is significantly different when the variability in velocities is low. The basalt velocities have 16th and 84th percentile points that are smaller and larger than their mean values by 2% to 10%. The interbed velocities have corresponding relative errors ranging from approximately 10%
to 20%, excepting the deepest Mabton interbed for which the relative error is only 1%. Given the scatter of the travel-time data within this interbed, especially in boreholes C4993 and C4997 (see Figure 3.10),
Table 6.3. Comparison of Average Vs from Redpath and Redpath and Texas Combined Stratigraphic Unit
EMM RRI PM
Redpath Shear Wave Velocities in Elephant Mountain Member, Rattlesnake Ridge Interbed, and Pomona Member
Geometric mean (ft/sec) 8163 3076 8297
84th percentile (ft/sec) 8454 3348 8568
16th percentile (ft/sec) 7883 2826 8035
Approx. Vel. Std. Dev. (ft/sec) 286 261 267
Sigma 0.035 0.085 0.032
Mult. Factor 1.036 1.088 1.033
Algebraic mean (ft/sec) 8167 3083 8300
84th percentile (ft/sec) 8455 3340 8565
16th percentile (ft/sec) 7878 2827 8035
Std. Dev. (ft/sec) 289 257 265
Harmonic mean (ft/sec) 8160 3069 8294
84th percentile (ft/sec) 8453 3357 8572
16th percentile (ft/sec) 7887 2826 8034
Approx. Vel. Std. Dev. (ft/sec) 283 264 269
Mult. Fac. High 1.036 1.094 1.033
Mult. Fac. Low 0.967 0.921 0.969
Redpath and Texas Shear Wave Velocities in Elephant Mountain Member, Rattlesnake Ridge Interbed, and Pomona Member
Geometric mean (ft/sec) 7863 2910 8298
84th percentile (ft/sec) 8385 3261 8487
16th percentile (ft/sec) 7374 2597 8114
Approx. Vel. Std. Dev. (ft/sec) 505 332 186
Sigma 0.064 0.114 0.022
Mult. Factor 1.066 1.121 1.023
Algebraic mean (ft/sec) 7877 2925 8300
84th percentile (ft/sec) 8370 3244 8485
16th percentile (ft/sec) 7383 2606 8115
Std. Dev. (ft/sec) 493 319 185
Harmonic mean (ft/sec) 7850 2894 8297
84th percentile (ft/sec) 8404 3284 8488
16th percentile (ft/sec) 7364 2586 8113
Approx. Vel. Std. Dev. (ft/sec) 518 344 187
Mult. Fac. High 1.071 1.135 1.023
Mult. Fac. Low 0.938 0.894 0.978
EMM = Elephant Mountain Member; RRI = Rattlesnake Ridge interbed; PM = Pomona Member.
Table 6.4. Comparison of Average Shear Wave Velocities for All Texas-Measured Basalt Velocities to Average Without Elephant Mountain Member, and Average for All Texas-Measured Interbed Velocities
All Basalt Velocities Except Elephant Mountain Member
All Basalt Velocities
All Interbed Velocities
Geometric mean (ft/sec) 8266 8112 2778
84th percentile (ft/sec) 8640 8617 3088
16th percentile (ft/sec) 7908 7637 2499
Approx. Vel. Std. Dev. (ft/sec) 366 490 294
Sigma 0.044 0.060 0.106
Mult. Factor 1.045 1.062 1.112
Algebraic mean (ft/sec) 8273 8126 2793
84th percentile (ft/sec) 8632 8601 3102
16th percentile (ft/sec) 7914 7650 2483
St. Dev. (ft/sec) 359 476 310
Harmonic mean (ft/sec) 8258 8098 2764
84th percentile (ft/sec) 8649 8636 3076
16th percentile (ft/sec) 7901 7624 2510
Approx. Vel. Std. Dev. (ft/sec) 373 504 280
Mult. Fac. High 1.047 1.066 1.113
Multi. Fac. Low 0.957 0.941 0.908